An adaptive filter is a computational device that attempts to model the relationship between two signals in real time in an iterative manner.
Such adaptive filters are used in many applications e.g. for canceling undesired signal components. Echo cancelers/equalizer (for inter-symbol interference cancellation) are a typical application of the adaptive filter for canceling an echo resulting from the trans-hybrid coupling of a hybrid circuit with an echo replica derived from the input signal of the adaptive filter. Adaptive filters are often realized either as a set of program instructions running on an arithmetical processing device such as a microprocessor or DSP chip, or as a set of logic operations implemented in a field-programmable gate array (FPGA) or in a semicustom or custom VLSI integrated circuit.
The adaptive filter has a tapped-delay line and a tap-weight coefficient controller for producing a sum of tap signals weighted respectively by tap-weight coefficients. According to a known adaptive convergence algorithm such as the LMS (least mean square) algorithm, the tap-weight (filter) coefficients are updated by correlations between the tap signals and a residual error of a correction signal, which is represented by the sum of the weighted tap signals.
Fast convergence of the tap-weight coefficients are of primary concern for designing an adaptive filter. In particular fast convergence at adaptive filters using resource sharing is a major desire in view of power efficient implementation for a cost sensitive market.